In spectral methods, the connectivity of \(\mathcal {G}\)  is usually described by means of the graph Laplacian matrix \(\mathbf {L} \in \mathbb {R}^{n \times n}\) . The graph Laplacian matrix \(\mathbf {L}\)  is a symmetric, positive semi-definite
and diagonally dominant matrix whose spectral properties reveal a number of important topological properties of the graph [1]}, [2]}.
It is defined in terms of the adjacency matrix \(\mathbf {W}\in \mathbb {R}^{n\times n}\) 
and the diagonal degree matrix \(\mathbf {D}\in \mathbb {R}^{n\times n}\)  \(\left( d_{ii} = \sum _{j = 1}^n w_{ij} \right)\)  as \(\Delta _2 = \mathbf {L} = \mathbf {D} - \mathbf {W}\)  (Figure REF ).
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